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Popular >

-cos(x)+4cos(2x)=0

Solution

- cos (x) + 4 cos (2 x) = 0

Solution

x = 0.68824 \dots + 2 πn, x = 2 π - 0.68824 \dots + 2 πn, x = 2.27491 \dots + 2 πn, x = - 2.27491 \dots + 2 πn

+1

Solution steps

- cos (x) + 4 cos (2 x) = 0

Rewrite using trig identities

- cos (x) + (- 1 + 2 cos^{2} (x)) \cdot 4 = 0

Solve by substitution

cos (x) = \frac{1 + 129}{16}, cos (x) = \frac{1 - 129}{16}

cos (x) = \frac{1 + 129}{16} : x = arccos (\frac{1 + 129}{16}) + 2 πn, x = 2 π - arccos (\frac{1 + 129}{16}) + 2 πn

cos (x) = \frac{1 - 129}{16} : x = arccos (\frac{1 - 129}{16}) + 2 πn, x = - arccos (\frac{1 - 129}{16}) + 2 πn

Combine all the solutions

x = arccos (\frac{1 + 129}{16}) + 2 πn, x = 2 π - arccos (\frac{1 + 129}{16}) + 2 πn, x = arccos (\frac{1 - 129}{16}) + 2 πn, x = - arccos (\frac{1 - 129}{16}) + 2 πn

Show solutions in decimal form

x = 0.68824 \dots + 2 πn, x = 2 π - 0.68824 \dots + 2 πn, x = 2.27491 \dots + 2 πn, x = - 2.27491 \dots + 2 πn

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